This article analyzes the influence of the saturation limiter used with dc-link voltage control (DVC) on the transient stability of grid-forming (GFM) inverters and proposes a flexible saturation limiter to alleviate its adverse impact. First, it is found that the conventional saturation limiter (CSL) can enhance transient stability. Yet, it would boost the dc-link voltage or even trigger overvoltage protection, especially when the threshold value of CSL is small. To tackle the adverse impact of CSL on dc-link voltage, a flexible saturation limiter is proposed, which only begins to limit the active power reference when the derivative of dc-link voltage turns from positive to negative (the dc-link voltage reaches its peak value at this instant). Finally, experimental tests confirm the effectiveness of the scheme.